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2
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0answers
30 views

Fourier spectrum reflected across origin and Nyquist frequency

Recently I've been trying to figure out what's the point of negative frequencies produced by the fourier transform. One answer was it's just there to make calculations more elegant. It could be ...
0
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1answer
28 views

integration and convolution

Please can some one help me on the following integration. $$ G(\nu)=\frac{1}{\Delta t}\int_{t_a - \frac{\Delta t}{2}}^{t_a + \frac{\Delta t}{2}} f(t_a -t)e^{-2\pi\nu it}dt $$ where ...
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0answers
14 views

Can wavelets be used for texture discrimination?

I've recently been studying wavelet analysis with a view to differentiating certain areas of texture images where the texture differs from the background pattern (which is quite random); for example a ...
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0answers
18 views

Simple proof for a continuous-time linear system and impulse $\delta$?

From Schaum's Outlines of Signals & Systems: Let's work with continuous-time signals. Let $T$ be a linear time-invariant system (LTI). Input $x(t)$ can be expressed as $x(t) = ...
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0answers
10 views

Scaling for Matlab fft operation?

I have a $N$ complex signal samples (QPSK) and I am creating an OFDM signal. When I am doing a IFFT operation in matlab, I use following command: $$Y=(dft/sqrt(N))*ifft(X),$$ where $X$ is the input ...
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0answers
17 views

interpreting the multivariate Kalman filter update equations

consider a multi-dimensional Kalman filter model with these state transition and measurement probabilities: $P(x_{t+1} | x_{t}) = Normal(Fx_{t}, \Sigma_{x})$ $P(z_{t} | x_{t}) = Normal(Hx_{t}, ...
1
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1answer
484 views

Calculate phase and amplitude of a sampled sine wave

I have an electronics project where I sample two sine waves. I would like to know what the amplitude (peak) and difference in phase is. Actually I just need to know the average product of the two ...
0
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0answers
34 views

Mathematically compare two sets of oscillatory data

I need to compare two sets of oscillatory data from a biological process. The data is quite noisy. Both sets have a similar frequency spectrum. I wonder what is the appropriate mathematical tool to ...
0
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0answers
17 views

Calculate f(t) if I have its power spectral density

I have a power spectral density of a function, which is S(w) = 1/(1+w²) + d(w-2) + d(w+2) W is omega (rad) d is an impulse I want to calculate f(t) which is the signal that has this power spectral ...
1
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1answer
30 views

Why is $\cos((\omega+\alpha\cos(\omega' t))t)$ the wrong model for frequency modulation?

So I was trying to program vibrato, or freqency modulation, naively using the model: $$\cos((\omega + \alpha\cos(\omega' t))t)$$ Where $\alpha \lt \omega$ and $\omega' \ll \omega$. For practical ...
0
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0answers
32 views

Nyquist–Shannon Sampling Theorem Counter Example?

I was learning about the Nyquist theorem regards signal processing the area of interest which I will rephrase below: Given a signal lasting infinitely long with a maximum frequency of f, then you can ...
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0answers
73 views

integral with respect to the point measure [closed]

We have integral $$\int_0^tf(t-u)dX(u)$$ where $X(u)$ is random point process( or at least renewal process). Also it is known that $f(t)\sim t^{-\alpha},$ $0<\alpha<1$ as $t\rightarrow \infty$. ...
3
votes
2answers
28 views

Discrete Time Fourier Transform of the signal represented by $x[n] = n^2 a^n u[n]$

I have a homework problem that I am just not sure where to start with. I have to take the Discrete Time Fourier Transform of a signal represented by: $$x[n] = n^2 a^n u[n]$$ given that $|a| < ...
1
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2answers
2k views

time derivative of discrete data in simulink

I'm implementing a program in Java that was delivered in Simulink. My expertise is limited, and I'm stuck on converting a derivative block. The simulink code applies a du/dt block to the input data. ...
0
votes
1answer
27 views

How are sinusoids and roots of unity related to each other?

The discrete Fourier transform (DFT) is often teached as being a transform that decomposes a given signal or sequence of numbers into sinusoids with frequencies $\large\frac{k}{N}$ where $k \in [0, ...
3
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1answer
19 views

Is this function/series periodic?

$$f(t)=\sum_{k=-\infty}^{\infty}(-1)^kp_{0.5}(t-2k)$$ Recall: $$p_{\Delta}=\begin{cases}\frac{1}{\Delta},&0\leq t\leq\Delta\\0&\text{ otherwise.}\end{cases}$$ Is the function periodic? If ...
0
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0answers
9 views

EZW parent-child relation

I’m trying to learn the EZW principle. I’m having trouble understanding the parent-child relationship. In my case, I want to use it on a 1 dimensional signal. So, let’s say for example a signal of 4 ...
2
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5answers
286 views

Compressive sensing with non square matrices

I'm implementing the algorithm in the following paper: "Compressive sensing for wideband cognitive radios" http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04218361 However I've run into a ...
1
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1answer
28 views

Absolute value in exponential, signal energy?

How can this give this result? Isn't the absolute of $(e^(-2*t))$ always 1?
1
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0answers
10 views

Detection theory - Sensitivity, Specificity - in Multi-Detection scenario

I am working in computer vision and have this scenario: For each frame of a video sequence I have the following: Image with a resolution of width * height discrete pixel locations. List of ...
2
votes
2answers
523 views

Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
0
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1answer
717 views

DSP, discrete time, how to calculate the frequency

this is from Digital Signal Processing, 4th ed, Sanjit K Mitra, problem 2.39b. The question is: Determine the fundamental period of $x[n] = cos(0.6n\pi + 0.3\pi)$ Since x[n], is in square brackets, ...
0
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1answer
312 views

What is a moving average system?

Can someone elaborate on what a moving average system is? I know that the system is defined as: $$y[n] = \frac{x[n] + x[n-1] + x[n-2]}{3}$$ How would we draw $y[n]$ given that we have a graph with ...
2
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1answer
28 views

Show that for a real impulse response function the response to a sine input is …

Working on this problem on linear invariant systems in signal processing, but unsure if I've got the right answer: Show that for a real impulse response function of $H(\omega)$, the response to a ...
0
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1answer
51 views

Which topics in maths should I know before I dive into programming for image processing?

I am a student who wants to start out with programming for Image processing but as I do not have a good mathematical background(I haven't studied A-level Maths) I would like to know what are the ...
10
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1answer
338 views

Creating intuition about Laplace & Fourier transforms

I've been reading up a bit on control systems theory, and needed to brush up a bit on my Laplace transforms. I know how to transform and invert the transform for pretty much every reasonable function, ...
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2answers
49 views

Changing a sigmoid curve to have an adjustable point of inflection

I am trying to an implement an adjustable Sigmoid curve such as in the YouTube video here. I found a potentially good candidate: $$f_k(x) = \frac{\left(x-x\cdot k\right)}{k-\left|x\right|\cdot 2\cdot ...
1
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0answers
37 views

a window slides over a sinusoid, which calculation on window of length p/4 always returns a maximum value compared to other window lengths?

We have a set of discretely sampled points that are on a sinusoid, in this case its period is 40: If we have windows of different lengths that slide over this time series, like this little ...
0
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1answer
894 views

Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
3
votes
3answers
2k views

Adjustable Sigmoid Curve (S-Curve) from $(0,0)$ to $ (1,1)$

I feel like this is such a simple question but I am at such a loss. I currently have a set of values that I would like to weigh by an S Curve. My data ranges from $0$ to $1$ and never leaves those ...
2
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1answer
111 views

Convolution of sine and unit step function

I started studying signal convolution recently and the first sample problem I got is to find convolution of sine and unit step function (Heaviside function). Here is what I have right now. ...
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0answers
45 views

How to calculate wavelet energy?

Part of my assignment about signal processing says the following: Compute the Discrete Wavelet Transform for the input signals Group the wavelet coefficients in trees growing across scales ...
0
votes
1answer
105 views

Implementing 1D Discrete Wavelet Transform in Matlab

I'm trying to write my own version of the Discrete Wavelet Transform using the bior4.4 filters. I think my implementation is not properly working yet, because whenever I input a signal and a number ...
3
votes
2answers
63 views

Laplace transform of $f(t)=te^{-t}\sin(2t)$

I was asked to find the Laplace transform of the function $\displaystyle f(t)=te^{-t}\sin(2t)$ using only the properties of Laplace transform, meaning, use clever tricks and the table shown at ...
0
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2answers
17 views

Why is the maximum value of cross-correlation achieved at similar section?

I'm a bit confused and probably need some sleep. When trying to find a short signal inside a long one (or the delay), it's almost a trivial fact that we should look for the maximal valued coefficient ...
2
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0answers
20 views

How to reconstruct a sparsely sampled multiperiodic function?

I have $m$ oscillators, where $m$ is unknown, with periods $\vec p = p_1, p_2, \ldots, p_{m}$. Each of the oscillators $j$ has associated with it a vector of sine coefficients $\vec A_j$ and angle ...
0
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1answer
32 views

Is this signal band-limited?

I'm self-learning signal processing now, and I've run into this question about band-limited signals: Consider the signal $x(t) = 1$ for $0 \leq t \leq T$ and $0$ otherwise. I've found that its ...
0
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0answers
28 views

The probability that a process signals (simple conditional probability)

I have this problem (from Montgomery's Applied Probability and Statistics, 5th Edition, problem 2-145, if anyone wants to see the original problem) but it's long, so for the sake of brevity I'll give ...
1
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0answers
115 views

Improvement of Minimum description length (MDL) estimate.

I earnestly request apology if this question is inappropriate for the forum. The question has two parts one technical and the other is not technical. I would appreciate any response. Let me consider ...
1
vote
1answer
37 views

Why is a wave with high FM aperiodic?

I was playing with sound synthesis in a program I wrote and I had a wave of the form $\sin(2\cdot\pi\cdot(f_c+\sin(2\cdot\pi\cdot f_m \cdot t)) \cdot t) $ So, just simple frequency modulation. When ...
0
votes
1answer
82 views

From Orthogonal vectors to Useful Bivector

If we have set of orthogonal vectors (X) can we form a set of orthogonal bivectors from that set? I am trying to find if there is a way to get 'more information' from an orthogonal matrix by some ...
0
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2answers
52 views

Sufficiently rich signals

I know that a signal is sufficiently rich of order $n$ when it "includes" at least $\dfrac{n}{2}$ different frequencies. This is intuitive when we are talking about a sine but what about other kind of ...
2
votes
1answer
23 views

Finding the coefficients of an MA(1) process given the expectation and variance.

The following is preparation of an exam I have coming up, any help would be appreciated. An MA(1) process is selected to model a stationary time series $\{ X_t \}$. We are given the lag one ...
0
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2answers
52 views

Gaussian noise generation with Matlab

I am a Matlab beginner & need to understand what is going on this code. I know it is for Gaussian noise generation, but what do these variables mean mathematically? ...
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1answer
26 views

Minimum Phase Filter

Suppose we want to find the minimum phase filter of a causal system with system function $H(z)=z^{-1}−0.3$. The minimum phase filter is $H_1(z)=1−0.3z^{−1}$ (by taking the zero to its conjugate ...
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1answer
48 views

How to derive the process noise co-variance matrix Q in this Kalman Filter example?

How to understand the process co-variance matrix Q in the example below ( I extracted it from Wikipedia http://en.wikipedia.org/wiki/Kalman_filter ) Consider a truck on perfectly frictionless, ...
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0answers
23 views

recovering of time series in SSA

i am trying to reconstruct time series from SSA ,because according to this link http://en.wikipedia.org/wiki/Singular_spectrum_analysis there is procedure ...
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0answers
38 views

Sine wave from fos + simple signal

I have a first order system $\frac {1}{(s+c)}$ and a signal of the form $\sum_{k=0}^\infty (-1)^{k}e^{-2ks}a(\frac{1-e^{-2s}}{s}- be^{-s}(\frac{1-e^{-s}}{s^2})) $ i.e a periodic signal of a square ...
2
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0answers
33 views

Fourier transform on trig wave

Find the fourier transform for signal in this picture (sorry for the bad quality) Could it be done like this? The signal is a sum of two triangular waves that are each delayed. ...
0
votes
1answer
36 views

exponential term evaluation doesn't make sense in this example

I am studying for my final and doing some practice questions, but I am confused by something: Here the solution says k at 0 we get N/2, but there is no way that answer is correct. If k is at 0 the ...